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"Hipolit Cegielski Hipolit Cegielski (6 January 1813, Ławki – 30 November 1868, Posen (Poznań), Kingdom of Prussia) was a Polish businessman and social and cultural activist. He founded H. Cegielski – Poznań in 1846. References * Witold Jakóbczyk, Przetrwać na Wartą 1815-1914, Dzieje narodu i państwa polskiego, vol. III-55, Krajowa Agencja Wydawnicza, Warszawa 1989 External links * 1815 births 1868 deaths People from Trzemeszno 19th-century Polish businesspeople People from the Grand Duchy of Posen People from the Province of Posen Members of the Prussian House of Representatives "
"Dezydery Chłapowski Baron Dezydery Chłapowski (1788 in Turew – 27 March 1879) of the Dryja coat of arms was a Polish general, businessman and political activist. Napoleon wounded before Ratisbon (1809), C.Gautherol. Chłapowski in a lancer uniform of the Imperial Guard is on the right. Life His father Józef Chłapowski (born 1756, died 1826) was the baron of Kościan County and his mother Urszula was from the Moszczeńska family. His tutor as a child was the French immigrant priest Steinhoff. He began his education at the Piarists university in Rydzyna and then in Berlin. At the age of 14, his father placed him in the Prussian dragoon regiment of General Bruesewitz that was stationed in Greater Poland. At the same time the young soldier studied at the Berlin Inspection Officers Institute, which he graduated from in 1805 with a promotion to lieutenant. He sought exemption from participating in the wars with Napoleonic France in 1806. After the occupation of Berlin by the French, he left for Poznań . Here he joined the hundred-man honor guard of Emperor Napoleon formed by the local nobility after the Greater Poland Uprising of 1806 under the command of Umiński. During this period he gained favor with Napoleon, who appointed him a lieutenant. During the campaign in 1807, he fought in a voltaic company in the 9th Infantry Regiment commanded by General Fr. Antoni Paweł Sułkowski formed in Gniezno . Decorated after the battle of Tczew , as a half-company commander, the Virtuti Militari cross and the Legion_of_Honour. During the siege of Gdańsk he was captured by Prussia. After a peace in Tylża and returning from Riga , where he was interned, he was promoted (1 August) to captain and assigned as adjutant to General Jan Henryk Dąbrowski . In February 1808 he was summoned to Paris , where he became the orderly officer of Napoleon. During this stay, he graduated from military studies at the Paris Polytechnic School. He passed the final exams before General Bertrand . He went through Spanish and Austrian campaigns alongside Napoleon. For participating in the battle of Regensburg he was awarded the title of baron of the empire. In January 1811he was appointed the head of the Polish squadron of the 1st Cavalry Regiment of the Imperial Guard . With him he carried out the Moscow ( 1812 ) and Saxon ( 1813 ) campaigns . During the latter, in Dresden, he asked for dismissal, which he obtained on 19 June . The decision was caused by Chłapowski's bitterness over Napoleon's attitude towards Poland (plans to give the Duchy of Warsaw to the tsar in exchange for peace) and the hardships of the campaigns he had gone through. Among the Napoleonic veterans, however, this action was badly received with accusations of desertion. As a retired colonel , he left for Paris. After the abdication of Napoleon, he went to Great Britain . During the "one hundred days of Napoleon "through Paris returned to Greater Poland ( 1815 ). Dezydery Chłapowski as Napoleon's staff officer He settled in his hometown Turwia, which he and Rąbin bought back from the debtor father of a professor, and then tidied up the property and began introducing a modern economy. To deepen their knowledge once again went on a trip to England ( 1818 - 1819 ), where among other things practiced physically working on the farm. Upon his return, he introduced solutions observed in England. Thanks to this, he repaid debts within 15 years and the property in Turwia quickly became one of the best farms in the Grand Duchy of Poznań . Chłapowski among others he introduced crop rotation instead of three- crop , used an iron plow and sowed soil enrichmentclover . As a result, Chłapowski was one of the guests invited to a conference in Berlin, where a plan of enfranchisement of peasants in the Grand Duchy was developed. He, for his part, allocated some of his land to parcel among peasants. In 1821 he married Antonina née Grudziński , sister of the Łowicz duchess Joanna , wife of the grand prince Konstanty . He was a deputy from the knighthood from the Kościan poviat to the provincial parliament of the Grand Duchy of Poznań in 1827 [1] and in 1830 [2] . He was a co-founder and activist of Credit Land and Fire Insurance Association. Palace in Turwia Baron Chłapowskis' coat of arms (French empire) Polish noble Dryja coat of arms When the November Uprising broke out, he put on his uniform again and crossed the border, reporting to the Polish insurgent army. He has developed a bold and interesting offensive plan, including capture of Brest on the Bug , but it was not approved by Józef Chłopicki , the dictator of the uprising , who preferred defensive tactics. It was only after the removal of Chłopicki that Chłapowski received the command of the brigade. He took part in the battle of Grochów , in which he himself headed the charge of the cavalry holding back Russian infantry after the withdrawal of Polish infantry. Then, under the command of the inept general Antoni Giełgud, he took part in the expedition to Lithuania during which he was promoted to the rank of Brigadier General . Despite a number of minor victories, Giełgud's indecision about Chłapowski's offensive plans for a quick attack on Vilnius before the arrival of major Russian forces led to the defeat of the expedition to Lithuania. By decision of the National Council, Chłapowski was finally promoted to the rank of division general and was entrusted with the supreme command in Lithuania, but it did not arrive in time (Chłapowski found out about it only in Prussia). The unit was forced to cross the Prussian-Russian border, where Chłapowski, as a Prussian subject, was sentenced to one year in prison. He avoided confiscating the property and the punishment was instead converted into a high fine. He served his sentence in a fortress in Szczecin , where he wrote a textbook On agriculture. After being released, he returned to Turwia. He was politically associated with his former subordinate Karol Marcinkowski . In the years 1838 - 1845 worked with the Guide Agricultural and Industrial , which posted articles of agriculture. He intended to set up an Agricultural University , which was to educate numerous apprentices at the Turkish estate. Among them were later activists such as Maksymilian Jackowski . He was also a co-founder and publisher of Przegląd Poznański and Sunday School . Throughout his activities he laid the foundations of organic work, thereby resisting Germanization. He supported enterprises such as the Poznań Bazaar and the Scientific Assistance Society as well as credit societies. He was a member of the national parliament. Correspondent member of the Galician Economic Society (1846-1879) . During the Greater Poland Uprising of 1848, he organized insurgent troops in his powiat. After the fall of the Spring of Nations , in Greater Poland, he became a member of the upper house of the Prussian Parliament, the House of Lords. Despite his strictness and Catholic views, which discouraged some liberals from him , his achievements made him a widely respected person with a great impact on the community of Greater Poland . He died on March 27, 1879, and was buried in Rąbin next to the local church . In 1899, his son, Kazimierz , published his father's diaries. Major General from April 25, 2014 Dezydery Chłapowski is the patron of the Ground Forces Training Center in Wędrzyn . The general was also a promoter of mid-field tree plantings in Poland, which contributed to the economic success of his property and is still favorable to agriculture in this area [5] [6] . In order to preserve his agricultural and natural heritage, in 1992 and again in 2014, a Landscape Park was created around his estate in Turwia. Its special purpose is to preserve the system of mid-field plantings with "(...) high natural, landscape, scientific, didactic and cultural values". See also *History of Poland (1795–1918) References * Witold Jakóbczyk, Przetrwać na Wartą 1815-1914, Dzieje narodu i państwa polskiego, vol. III-55, Krajowa Agencja Wydawnicza, Warszawa 1989 External links *Dynastic genealogy *Ornatowski.com 1788 births 1879 deaths People from Kościan County Members of the Prussian House of Lords Members of the Sejm (Provinziallandtag) of Posen Polish generals People from the Grand Duchy of Posen People from the Province of Posen Greater Poland Uprising (1848) participants Barons of Poland Recipients of the Legion of Honour Recipients of the Virtuti Militari Polish commanders of the Napoleonic Wars Generals of the November Uprising Barons of the First French Empire "
"The left-handed orientation is shown on the left, and the right-handed on the right. In mathematics, orientation is a geometric notion that in two dimensions allows one to say when a cycle goes around clockwise or counterclockwise, and in three dimensions when a figure is left-handed or right-handed. In linear algebra, the notion of orientation makes sense in arbitrary finite dimension. In this setting, the orientation of an ordered basis is a kind of asymmetry that makes a reflection impossible to replicate by means of a simple rotation. Thus, in three dimensions, it is impossible to make the left hand of a human figure into the right hand of the figure by applying a rotation alone, but it is possible to do so by reflecting the figure in a mirror. As a result, in the three-dimensional Euclidean space, the two possible basis orientations are called right-handed and left-handed (or right-chiral and left-chiral). The orientation on a real vector space is the arbitrary choice of which ordered bases are "positively" oriented and which are "negatively" oriented. In the three-dimensional Euclidean space, right- handed bases are typically declared to be positively oriented, but the choice is arbitrary, as they may also be assigned a negative orientation. A vector space with an orientation selected is called an oriented' vector space, while one not having an orientation selected, is called '. Definition Let V be a finite-dimensional real vector space and let b1 and b2 be two ordered bases for V. It is a standard result in linear algebra that there exists a unique linear transformation A : V → V that takes b1 to b2. The bases b1 and b2 are said to have the same orientation (or be consistently oriented) if A has positive determinant; otherwise they have opposite orientations. The property of having the same orientation defines an equivalence relation on the set of all ordered bases for V. If V is non-zero, there are precisely two equivalence classes determined by this relation. An orientation on V is an assignment of +1 to one equivalence class and −1 to the other. Every ordered basis lives in one equivalence class or another. Thus any choice of a privileged ordered basis for V determines an orientation: the orientation class of the privileged basis is declared to be positive. For example, the standard basis on Rn provides a standard orientation on Rn (in turn, the orientation of the standard basis depends on the orientation of the Cartesian coordinate system on which it is built). Any choice of a linear isomorphism between V and Rn will then provide an orientation on V. The ordering of elements in a basis is crucial. Two bases with a different ordering will differ by some permutation. They will have the same/opposite orientations according to whether the signature of this permutation is ±1. This is because the determinant of a permutation matrix is equal to the signature of the associated permutation. Similarly, let A be a nonsingular linear mapping of vector space Rn to Rn. This mapping is orientation-preserving if its determinant is positive. For instance, in R3 a rotation around the Z Cartesian axis by an angle α is orientation-preserving: :: \mathbf {A}_1 = \begin{pmatrix} \cos \alpha & -\sin \alpha & 0 \\\ \sin \alpha & \cos \alpha & 0 \\\ 0 & 0 & 1 \end{pmatrix} while a reflection by the XY Cartesian plane is not orientation-preserving: :: \mathbf {A}_2 = \begin{pmatrix} 1 & 0 & 0 \\\ 0 & 1 & 0 \\\ 0 & 0 & -1 \end{pmatrix} Zero-dimensional case The concept of orientation degenerates in the zero-dimensional case. A zero-dimensional vector space has only a single point, the zero vector. Consequently, the only basis of a zero- dimensional vector space is the empty set \emptyset. Therefore, there is a single equivalence class of ordered bases, namely, the class \\{\emptyset\\} whose sole member is the empty set. This means that an orientation of a zero- dimensional space is a function :\\{\\{\emptyset\\}\\} \to \\{\pm 1\\}. It is therefore possible to orient a point in two different ways, positive and negative. Because there is only a single ordered basis \emptyset, a zero- dimensional vector space is the same as a zero-dimensional vector space with ordered basis. Choosing \\{\emptyset\\} \mapsto +1 or \\{\emptyset\\} \mapsto -1 therefore chooses an orientation of every basis of every zero-dimensional vector space. If all zero-dimensional vector spaces are assigned this orientation, then, because all isomorphisms among zero-dimensional vector spaces preserve the ordered basis, they also preserve the orientation. This is unlike the case of higher-dimensional vector spaces where there is no way to choose an orientation so that it is preserved under all isomorphisms. However, there are situations where it is desirable to give different orientations to different points. For example, consider the fundamental theorem of calculus as an instance of Stokes' theorem. A closed interval is a one-dimensional manifold with boundary, and its boundary is the set }. In order to get the correct statement of the fundamental theorem of calculus, the point should be oriented positively, while the point should be oriented negatively. On a line The one-dimensional case deals with a line which may be traversed in one of two directions. There are two orientations to a line just as there are two orientations to a circle. In the case of a line segment (a connected subset of a line), the two possible orientations result in directed line segments. An orientable surface sometimes has the selected orientation indicated by the orientation of a line perpendicular to the surface. Alternate viewpoints Multilinear algebra For any n-dimensional real vector space V we can form the kth-exterior power of V, denoted ΛkV. This is a real vector space of dimension \tbinom{n}{k}. The vector space ΛnV (called the top exterior power) therefore has dimension 1. That is, ΛnV is just a real line. There is no a priori choice of which direction on this line is positive. An orientation is just such a choice. Any nonzero linear form ω on ΛnV determines an orientation of V by declaring that x is in the positive direction when ω(x) > 0. To connect with the basis point of view we say that the positively-oriented bases are those on which ω evaluates to a positive number (since ω is an n-form we can evaluate it on an ordered set of n vectors, giving an element of R). The form ω is called an orientation form. If {ei} is a privileged basis for V and {ei∗} is the dual basis, then the orientation form giving the standard orientation is . The connection of this with the determinant point of view is: the determinant of an endomorphism T : V \to V can be interpreted as the induced action on the top exterior power. Lie group theory Let B be the set of all ordered bases for V. Then the general linear group GL(V) acts freely and transitively on B. (In fancy language, B is a GL(V)-torsor). This means that as a manifold, B is (noncanonically) homeomorphic to GL(V). Note that the group GL(V) is not connected, but rather has two connected components according to whether the determinant of the transformation is positive or negative (except for GL0, which is the trivial group and thus has a single connected component; this corresponds to the canonical orientation on a zero-dimensional vector space). The identity component of GL(V) is denoted GL+(V) and consists of those transformations with positive determinant. The action of GL+(V) on B is not transitive: there are two orbits which correspond to the connected components of B. These orbits are precisely the equivalence classes referred to above. Since B does not have a distinguished element (i.e. a privileged basis) there is no natural choice of which component is positive. Contrast this with GL(V) which does have a privileged component: the component of the identity. A specific choice of homeomorphism between B and GL(V) is equivalent to a choice of a privileged basis and therefore determines an orientation. More formally: \pi_0(\operatorname{GL}(V)) = (\operatorname{GL}(V)/\operatorname{GL}^+(V) = \\{\pm 1\\}, and the Stiefel manifold of n-frames in V is a \operatorname{GL}(V)-torsor, so V_n(V)/\operatorname{GL}^+(V) is a torsor over \\{\pm 1\\}, i.e., its 2 points, and a choice of one of them is an orientation. Geometric algebra thumbleft150pxParallel plane segments with the same attitude, magnitude and orientation, all corresponding to the same bivector . The various objects of geometric algebra are charged with three attributes or features: attitude, orientation, and magnitude. For example, a vector has an attitude given by a straight line parallel to it, an orientation given by its sense (often indicated by an arrowhead) and a magnitude given by its length. Similarly, a bivector in three dimensions has an attitude given by the family of planes associated with it (possibly specified by the normal line common to these planes ), an orientation (sometimes denoted by a curved arrow in the plane) indicating a choice of sense of traversal of its boundary (its circulation), and a magnitude given by the area of the parallelogram defined by its two vectors. Orientation on manifolds The orientation of a volume may be determined by the orientation on its boundary, indicated by the circulating arrows. Each point p on an n-dimensional differentiable manifold has a tangent space TpM which is an n-dimensional real vector space. Each of these vector spaces can be assigned an orientation. Some orientations "vary smoothly" from point to point. Due to certain topological restrictions, this is not always possible. A manifold that admits a smooth choice of orientations for its tangent spaces is said to be orientable. See also *Sign convention *Rotation formalisms in three dimensions *Chirality (mathematics) *Right-hand rule *Even and odd permutations *Cartesian coordinate system *Pseudovector -- Pseudovectors are a consequence of oriented spaces. *Orientability -- Discussion about the possibility of having orientations in a space. *Orientation of a vector bundle References External links * Linear algebra Analytic geometry Orientation (geometry) "